I like to think I would have sufficient courage to run from conscription, but at twice the age at which my father, the most pacific man I know, accepted his draft, I don't know I can state categorically that I would run in the same situation.
He hasn't told me much about actual combat, but a lot about how an army does what it does through a mixture of psychological manipulation and shouting. Conscription seems to work in the same way, with community and familial obligations outweighing the impulse to shie from a path you think abominable. Or to save your own sorry ass from doing your patriotic duty, as some would have it.
Tim O'Brien's short story "On the Rainy River" is the best explanation I have come across to date as to why more people don't run from a draft. It takes greater courage and resolve to leave everyone you care about behind you than it does to go to war.

The scenario posed does not actually offer a choice, a rational individual does not accept their own death (surrender, discovery) as a choice. The question although phrased as though there are two options really only offers one.